Topological superconductivity in monolayer transition metal dichalcogenides

Anisotropic Spin Fluctuations Induced by Spin-Orbit Coupling in a Misfit Layer Compound (LaSe)1.14(NbSe2)

Spin-orbit coupling (SOC) has significant effects on the superconductivity and magnetism of transition metal dichalcogenides (TMDs) at the 2D limit. Although 2D TMD samples possess many exotic properties different from those of bulk samples, experimental characterization in this field is still limited, especially for magnetism. Recent studies have revealed that bulk misfit layer compounds (MLCs) with (LaSe)1.14(NbSe2)n = 1,2 exhibit an Ising superconductivity similar to that of heavily electron-doped NbSe2 monolayers. This offers an opportunity to study the effect of SOC on the magnetism of 2D TMDs. Here, the possible SOC effect in (LaSe)1.14(NbSe2) is investigated by measuring nuclear magnetic resonance (NMR) and electrical transport. It is found that the LaSe layer not only functions as a charge reservoir for transferring electrons into the NbSe2 layer but also remarkably influences the local electronic environment around the 93Nb nuclei. More importantly, the significant SOC induces both a weak antilocalization (WAL) effect and anisotropic spin fluctuations in noncentrosymmetric NbSe2 layers. The present work contributes to a deep understanding of the role of the SOC effect in 2D TMDs and supports MCLs as an intriguing platform for exploring exotic physical properties within the 2D limit.

Realizing Topological Superconductivity in Tunable Bose-Fermi Mixtures with Transition Metal Dichalcogenide Heterostructures

Heterostructures of two-dimensional transition metal dichalcogenides are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling interlayer excitons to doped charges in a trilayer structure. Their interactions are determined by the interlayer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance.

Transformation of the crystal structure of Ni0.5TiSe2 under in situ heating

The crystal structure of the Ni0.5TiSe2 compound has been studied in situ in the temperature range of 25-1000 °C using synchrotron radiation X-ray diffraction. The previously known order-disorder transition in the Ni sublattice at ∼100 °C was found to be a second-order phase transition and belongs to the 3D Ising universality class. Reversible extraction of nickel selenides was observed in the temperature range of 275-975 °C. It was explained in terms of Ni extraction from Ni0.5TiSe2 due to the thermal widening of the Ni 3d/Ti 3d/Se 4p impurity band. The Ni-TiSe2 phase diagram follows the typical pattern of MxTiSe2 (M - transition metal) compounds.

Spotlight: Visualization of Moiré Quantum Phenomena in Transition Metal Dichalcogenide with Scanning Tunneling Microscopy

Transition metal dichalcogenide (TMD) moiré superlattices have emerged as a significant area of study in condensed matter physics. Thanks to their superior optical properties, tunable electronic band structure, strong Coulomb interactions, and quenched electron kinetic energy, they offer exciting avenues to explore correlated quantum phenomena, topological properties, and light-matter interactions. In recent years, scanning tunneling microscopy (STM) has made significant impacts on the study of these fields by enabling intrinsic surface visualization and spectroscopic measurements with unprecedented atomic scale detail. Here, we spotlight the key findings and innovative developments in imaging and characterization of TMD heterostructures via STM, from its initial implementation on the in situ grown sample to the latest photocurrent tunneling microscopy. The evolution in sample design, progressing from a conductive to an insulating substrate, has not only expanded our control over TMD moiré superlattices but also promoted an understanding of their structures and strongly correlated properties, such as the structural reconstruction and formation of generalized two-dimensional Wigner crystal states. In addition to highlighting recent advancements, we outline upcoming challenges, suggest the direction of future research, and advocate for the versatile use of STM to further comprehend and manipulate the quantum dynamics in TMD moiré superlattices.

Van Hove singularity driven enhancement of superconductivity in two-dimensional tungsten monofluoride (WF)

Superconductivity in two-dimensional materials has gained significant attention in the last few years. In this work, we report phonon-mediated superconductivity investigations in monolayer Tungsten monofluoride (WF) by solving anisotropic Migdal Eliashberg equations as implemented in EPW. By employing first-principles calculations, our examination of phonon dispersion spectra suggests that WF is dynamically stable. Our results show that WF has weak electron-phonon coupling (EPC) strength (λ) of 0.49 with superconducting transition temperature (Tc) of 2.6 K. A saddle point is observed at 0.11 eV below the Fermi level (EF) of WF, which corresponds to the Van Hove singularity (VHS). On shifting the Fermi level to the VHS by hole doping (3.7 × 1014cm-2), the EPC strength increases to 0.93, which leads to an increase in theTcto 11 K. However, the superconducting transition temperature of both pristine and doped WF increases to approximately 7.2 K and 17.2 K, respectively, by applying the Full Bandwidth (FBW) anisotropic Migdal-Eliashberg equations. Our results provide a platform for the experimental realization of superconductivity in WF and enhancement of the superconducting transition temperature by adjusting the position ofEFto the VHS.

Electronic and Crystal Structure of New CrxZrSe2 Intercalation Compounds

New intercalation compounds CrxZrSe2 were synthesized and thoroughly studied. Cr atoms were found to occupy the positions both tetrahedrally and octahedrally coordinated by the Se atoms in the interlayer gap. The magnetic properties and electrical resistivity were studied in the temperature ranges of 2.4-300 K and 80-340 K, respectively. The compounds change their behavior from semiconducting (x = 0.1) to metallic (x > 0.1). The magnetic interaction strongly depends on the Cr content and temperature. The spin-glass state with antiferromagnetic interaction exists at T < Tcrit for CrxZrSe2 with x ≤ 0.2, while at x ≥ 0.3 ferromagnetic contribution arises as well. The single crystals of CrxZrSe2 were grown to study the electronic structure of the materials. A combination of the X-ray photoelectron spectroscopy (including that across Cr 2p-3d and Zr 3p-4d resonance) and X-ray absorption spectroscopy methods allowed to propose the location of the Cr 3d-states in the Se 3p-Zr 4d energy gap.

Pressure-Induced Superconductivity and Topological Quantum Phase Transitions in the Topological Semimetal ZrTe2

Topological transition metal dichalcogenides (TMDCs) have attracted much attention due to their potential applications in spintronics and quantum computations. In this work, the structural and electronic properties of topological TMDCs candidate ZrTe2 are systematically investigated under high pressure. A pressure-induced Lifshitz transition is evidenced by the change of charge carrier type as well as the Fermi surface. Superconductivity is observed at around 8.3 GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum Tc of 5.6 K for ZrTe2 . Furthermore, the theoretical calculations suggest the presence of multiple pressure-induced topological quantum phase transitions, which coexists with emergence of superconductivity. The results demonstrate that ZrTe2 with nontrivial topology of electronic states displays new ground states upon compression.

High-throughput ab initio design of atomic interfaces using InterMatch

Forming a hetero-interface is a materials-design strategy that can access an astronomically large phase space. However, the immense phase space necessitates a high-throughput approach for an optimal interface design. Here we introduce a high-throughput computational framework, InterMatch, for efficiently predicting charge transfer, strain, and superlattice structure of an interface by leveraging the databases of individual bulk materials. Specifically, the algorithm reads in the lattice vectors, density of states, and the stiffness tensors for each material in their isolated form from the Materials Project. From these bulk properties, InterMatch estimates the interfacial properties. We benchmark InterMatch predictions for the charge transfer against experimental measurements and supercell density-functional theory calculations. We then use InterMatch to predict promising interface candidates for doping transition metal dichalcogenide MoSe2. Finally, we explain experimental observation of factor of 10 variation in the supercell periodicity within a few microns in graphene/α-RuCl3 by exploring low energy superlattice structures as a function of twist angle using InterMatch. We anticipate our open-source InterMatch algorithm accelerating and guiding ever-growing interfacial design efforts. Moreover, the interface database resulting from the InterMatch searches presented in this paper can be readily accessed online.

Orbital Fulde-Ferrell Pairing State in Moiré Ising Superconductors

In this Letter, we study superconducting moiré homobilayer transition metal dichalcogenides where the Ising spin-orbit coupling (SOC) is much larger than the moiré bandwidth. We call such noncentrosymmetric superconductors, moiré Ising superconductors. Because of the large Ising SOC, the depairing effect caused by the Zeeman field is negligible and the in-plane upper critical field (B_{c2}) is determined by the orbital effects. This allows us to study the effect of large orbital fields. Interestingly, when the applied in-plane field is larger than the conventional orbital B_{c2}, a finite-momentum pairing phase would appear which we call the orbital Fulde-Ferrell (FF) state. In this state, the Cooper pairs acquire a net momentum of 2q_{B}, where 2q_{B}=eBd is the momentum shift caused by the magnetic field B and d denotes the layer separation. This orbital field-driven FF state is different from the conventional FF state driven by Zeeman effects in Rashba superconductors. Remarkably, we predict that the FF pairing would result in a giant superconducting diode effect under electric gating when layer asymmetry is induced. An upturn of the B_{c2} as the temperature is lowered, coupled with the giant superconducting diode effect, would allow the detection of the orbital FF state.

Laser-Synthesized 2D-MoS2 Nanostructured Photoconductors

The direct laser synthesis of periodically nanostructured 2D transition metal dichalcogenide (2D-TMD) films, from single source precursors, is presented here. Laser synthesis of MoS₂ and WS₂ tracks is achieved by localized thermal dissociation of Mo and W thiosalts, caused by the strong absorption of continuous wave (c.w.) visible laser radiation by the precursor film. Moreover, within a range of irradiation conditions we have observed occurrence of 1D and 2D spontaneous periodic modulation in the thickness of the laser-synthesized TMD films, which in some cases is so extreme that it results in the formation of isolated nanoribbons with a width of ~200 nm and a length of several micrometers. The formation of these nanostructures is attributed to the effect that is known as laser-induced periodic surface structures (LIPSS), which is caused by self-organized modulation of the incident laser intensity distribution due to optical feedback from surface roughness. We have fabricated two terminal photoconductive detectors based on nanostructured and continuous films and we show that the nanostructured TMD films exhibit enhanced photo-response, with photocurrent yield increased by three orders of magnitude as compared to their continuous counterparts.

Superfluid response of an atomically thin gate-tuned van der Waals superconductor

A growing number of two-dimensional superconductors are being discovered in the family of exfoliated van der Waals materials. Due to small sample volume, the superfluid response of these materials has not been characterized. Here, we use a local magnetic probe to directly measure this key property of the tunable, gate-induced superconducting state in MoS₂. We find that the backgate changes the transition temperature non-monotonically whereas the superfluid stiffness at low temperature and the normal state conductivity monotonically increase. In some devices, we find direct signatures in agreement with a Berezinskii-Kosterlitz-Thouless transition, whereas in others we find a broadened onset of the superfluid response. We show that the observed behavior is consistent with disorder playing an important role in determining the properties of superconducting MoS₂. Our work demonstrates that magnetic property measurements are within reach for superconducting devices based on exfoliated sheets and reveals that the superfluid response significantly deviates from simple BCS-like behavior.

Pair-Density-Wave and Chiral Superconductivity in Twisted Bilayer Transition Metal Dichalcogenides

We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe_{2}) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N=1, 2, 4 (namely, p+ip, d+id, and g+ig) appear over a large parameter region with a moiré filling factor around n=1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized superconducting diode effect.

Superconductivity in Te-Deficient ZrTe2

We present structural, electrical, and thermoelectric potential measurements on high-quality single crystals of ZrTe_1.8 grown from isothermal chemical vapor transport. These measurements show that the Te-deficient ZrTe_1.8, which forms the same structure as the nonsuperconducting ZrTe₂, is superconducting below 3.2 K. The temperature dependence of the upper critical field (H _c2) deviates from the behavior expected in conventional single-band superconductors, being best described by an electron-phonon two-gap superconducting model with strong intraband coupling. For the ZrTe_1.8 single crystals, the Seebeck potential measurements suggest that the charge carriers are predominantly negative, in agreement with the ab initio calculations. Through first-principles calculations within DFT, we show that the slight reduction of Te occupancy in ZrTe₂ unexpectedly gives origin to density of states peaks at the Fermi level due to the formation of localized Zr-d bands, possibly promoting electronic instabilities at the Fermi level and an increase at the critical temperature according to the standard BCS theory. These findings highlight that the Te deficiency promotes the electronic conditions for the stability of the superconducting ground state, suggesting that defects can fine-tune the electronic structure to support superconductivity.

Superconductivity and density-wave fluctuations in an extended triangular Hubbard model: an application to SnSe2

We employ the fluctuation-exchange approximation to study the relation of superconducting pairing symmetries and density-wave fluctuations based on the extended triangular Hubbard model upon electron doping and interactions, with an possible application to the layered metal dichalcogenide SnSe₂. For the case where the interactions between electrons contain only the on-site Hubbard term, the superconducting pairings are mainly mediated by spin fluctuations, and the spin-singlet pairing with thed-wave symmetry robustly dominates in the low and moderate doping levels, and ad-wave to extendeds-wave transition is observed as the electron doping reachesn = 1. When the near-neighbor site Coulomb interactions are also included, the charge fluctuations are enhanced, and the spin-triplet pairings with thep-wave andf-wave symmetries can be realized in the high and low doping levels, respectively.

Crossover from Ising- to Rashba-type superconductivity in epitaxial Bi2Se3/monolayer NbSe2 heterostructures

A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host topological superconductivity. Although the growth of epitaxial TI films on s-wave superconductors has been achieved by molecular-beam epitaxy, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the topological superconducting phase. Here we used molecular-beam epitaxy to grow Bi₂Se₃ films with a controlled thickness on monolayer NbSe₂ and performed in situ angle-resolved photoemission spectroscopy and ex situ magnetotransport measurements on these heterostructures. We found that the emergence of Rashba-type bulk quantum-well bands and spin-non-degenerate surface states coincides with a marked suppression of the in-plane upper critical magnetic field of the superconductivity in Bi₂Se₃/monolayer NbSe₂ heterostructures. This is a signature of a crossover from Ising- to Rashba-type superconducting pairings, induced by altering the Bi₂Se₃ film thickness. Our work opens a route for exploring a robust topological superconducting phase in TI/Ising superconductor heterostructures.

Multivalley Superconductivity in Monolayer Transition Metal Dichalcogenides

In transition metal dichalcogenides (TMDs), Ising superconductivity with an antisymmetric spin texture on the Fermi surface has attracted wide interest due to the exotic pairing and topological properties. However, it is not clear whether the Q valley with a giant spin splitting is involved in the superconductivity of heavily doped semiconducting 2H-TMDs. Here by taking advantage of a high-quality monolayer WS₂ on hexagonal boron nitride flakes, we report an ionic-gating induced superconducting dome with a record high critical temperature of ∼6 K, accompanied by an emergent nonlinear Hall effect. The nonlinearity indicates the development of an additional high-mobility channel, which (corroborated by first principle calculations) can be ascribed to the population of Q valleys. Thus, multivalley population at K and Q is suggested to be a prerequisite for developing superconductivity. The involvement of Q valleys also provides insights to the spin textured Fermi surface of Ising superconductivity in the large family of transition metal dichalcogenides.

Janus structures of SMoSe and SVSe compositions with low enthalpy and unusual crystal chemistry

The recent synthesis of single-layer Janus-type transition metal dichalcogenides (TMDs) raises the question of the existence of other possible 2D structures with an asymmetric out-of-plane structural configuration. In the present work, a theoretical search for new Janus structures having SMoSe and SVSe compositions is performed. A detailed crystal-chemical analysis of the predicted structures is carried out, and it is shown that some of the dynamically stable structures are characterized by crystal-chemical features that are unique among TMDs, including quadruple Mo—Mo bonds and covalent S—S and Se—Se bonds. It is also shown that Mo-bearing TMDs have a tendency to form strong Mo—Mo bonds with chains or isolated dimers of molybdenum atoms, while in the case of vanadium-containing TMDs this feature is not characteristic. Two predicted crystal structures, called 1M-SVSe and 1A′-SMoSe, are especially promising for experimental synthesis and practical applications owing to their dynamical stability and rather low value of enthalpy compared with known structures. The enthalpy of 1M-SVSe is 0.22 eV per formula unit lower than that of 1T-SVSe, while the enthalpy of 1A′-SMoSe is 0.12 eV per formula unit lower than the enthalpy of 1T-SMoSe. The performed topological analysis showed that the predicted structures are unique and do not have analogues in the Inorganic Crystal Structure Database.

Nonunitary superconductivity in complex quantum materials

We revisit the concept of nonunitary superconductivity and generalize it to address complex quantum materials. Starting with a brief review of the notion of nonunitary superconductivity, we discuss its spectral signatures in simple models with only the spin as an internal degree of freedom. In complex materials with multiple internal degrees of freedom, there are many more possibilities for the development of nonunitary order parameters. We provide examples focusing on d-electron systems with two orbitals, applicable to a variety of materials. We discuss the consequences for the superconducting spectra, highlighting that gap openings of band crossings at finite energies can be attributed to a nonunitary order parameter if this is associated with a finite superconducting fitness matrix. We speculate that nonunitary superconductivity in complex quantum materials is in fact very common and can be associated with multiple cases of recently reported time-reversal symmetry breaking superconductors.

Observation of Coexisting Weak Localization and Superconducting Fluctuations in Strained Sn1-xInxTe Thin Films

Topological superconductors have attracted tremendous excitement as they are predicted to host Majorana zero modes that can be utilized for topological quantum computing. Candidate topological superconductor Sn_1-xIn_xTe thin films (0 < x < 0.3) grown by molecular beam epitaxy and strained in the (111) plane are shown to host quantum interference effects in the conductivity coexisting with superconducting fluctuations above the critical temperature T_c. An analysis of the normal state magnetoresistance reveals these effects. A crossover from weak antilocalization to localization is consistently observed in superconducting samples, indicating that superconductivity originates dominantly from charge carriers occupying trivial states that may be strongly spin-orbit split. A large enhancement of the conductivity is observed above T_c, indicating the presence of superconducting fluctuations. Our results motivate a re-examination of the debated pairing symmetry of this material when subjected to quantum confinement and lattice strain.

Role of Two-Dimensional Ising Superconductivity in the Nonequilibrium Quasiparticle Spin-to-Charge Conversion Efficiency

Nonequilibrium studies of two-dimensional (2D) superconductors (SCs) with Ising spin-orbit coupling are prerequisite for their successful application to equilibrium spin-triplet Cooper pairs and, potentially, Majorana Fermions. By taking advantage of the recent discoveries of 2D SCs and their compatibility with any other materials, we fabricate here nonlocal magnon devices to examine how such 2D Ising superconductivity affects the conversion efficiency of magnon spin to quasiparticle charge in superconducting flakes of 2H-NbSe₂ transferred onto ferrimagnetic insulating Y₃Fe₅O₁₂. Comparison with a reference device based on a conventionally paired superconductor shows that the Y₃Fe₅O₁₂-induced in-plane (IP) exchange spin-splitting in the NbSe₂ flake is hindered by its inherent out-of-plane (OOP) spin-orbit field, which, in turn, limits the transition-state enhancement of the spin-to-charge conversion efficiency. Our out-of-equilibrium study highlights the significance of symmetry matching between underlying Cooper pairs and exchange-induced spin-splitting for the giant transition-state spin-to-charge conversion and may have implications toward proximity-engineered spin-polarized triplet pairing via tuning the relative strength of IP exchange and OOP spin-orbit fields in ferromagnetic insulator/2D Ising SC bilayers.

Recent Advances in 2D Superconductors

The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (T_c ), continuous phase transition, and enhanced parallel critical magnetic field (B_c ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-T_c superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced B_c , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.

Tuning Molecular Superlattice by Charge-Density-Wave Patterns in Two-Dimensional Monolayer Crystals

Charge density wave (CDW) in two-dimensional (2D) crystals plays a vital role in tuning the interface structures and properties. However, how the CDW tunes the self-assembled molecular superlattice still remains unclear. In this study, we investigated the self-assembled manganese phthalocyanine (MnPc) molecular superlattice on single-layered 1T- and 2H-NbSe₂ crystals under regulation by distinct CDW patterns. We observe that, in low coverage, MnPc molecules preferentially adsorb on 2H-NbSe₂ compared to 1T-NbSe₂. With increasing coverage, MnPc can form a highly ordered superlattice on 2H-NbSe₂; however, it is randomly distributed on 1T-NbSe₂. We reveal a perfect geometric commensurability between the molecular superlattice and intrinsic CDW pattern in 2H-NbSe₂ and a poor commensurability for that of 1T-NbSe₂. We believe that the subtly different geometric commensurability dominates the different adsorption and arrangement of the molecular superlattices on 2D CDW patterns. Our study provides a pioneering approach for tuning the molecular superlattices using the CDW patterns.

P-type doping in 2M-WS2 for a complete phase diagram

2M-WS₂ as a new phase of transition metal dichalcogenides possesses many novel physical properties, such as superconductivity and topological surface states. The effect of n-type doping on the superconductivity of this material has been studied. However, p-type doping has not been studied, because it is difficult to implement p-type doping in metastable 2M-WS₂. In this paper, p-type doping was achieved in 2M-WS₂ for the first time by using Mo. With the increase of the Mo content, the carrier concentration rises slightly from 1.42 × 10²¹ cm^-1 to 1.56 × 10²¹ cm^-1. Meanwhile, the superconducting transition temperature decreases monotonously with the increase of Mo doping and reaches a minimum value of 4.37 K at the doping limit of x = 0.6 in W_1-xMo_xS₂. Combining the data of n-type doped 2M-WS₂ from our previous research, we summarize the carrier concentration and superconducting transition temperature in a phase diagram, which shows a typical dome-like shape. These results uncover the relationship between the carrier concentration and electronic state of 2M-WS₂.

Bending moduli for forty-four select atomic monolayers from first principles

We calculate bending moduli along the principal directions for forty-four select atomic monolayers using ab initio density functional theory (DFT). Specifically, considering representative materials from each of Groups IV, III-V, V monolayers, Group IV monochalcogenides, transition metal trichalcogenides, transition metal dichalcogenides and Group III monochalcogenides, we utilize the recently developed Cyclic DFT method to calculate the bending moduli in the practically relevant but previously intractable low-curvature limit. We find that the moduli generally increase with thickness of the monolayer, while spanning three orders of magnitude between the different materials. In addition, structures with a rectangular lattice are prone to a higher degree of anisotropy relative to those with a honeycomb lattice. Exceptions to these trends are generally a consequence of unusually strong/weak bonding and/or significant structural relxation related effects.

Inversion-Protected Higher-Order Topological Superconductivity in Monolayer WTe_{2}

Monolayer WTe_{2}, a centrosymmetric transition metal dichacogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we study the pairing symmetry and topological nature of superconducting WTe_{2} with a microscopic model at mean-field level. Surprisingly, we find that the spin-triplet phases in our phase diagram all host Majorana modes localized on two opposite corners. Even when the conventional pairing is favored, we find that an intermediate in-plane magnetic field exceeding the Pauli limit stabilizes an unconventional equal-spin pairing aligning with the field, which also hosts Majorana corner modes. Motivated by our findings, we obtain a recipe for two-dimensional superconductors featuring "higher-order topology" from the boundary perspective. Generally, a superconducting inversion-symmetric quantum spin Hall material whose normal-state Fermi surface is away from high-symmetry points, such as gated monolayer WTe_{2}, hosts Majorana corner modes if the superconductivity is parity-odd. We further point out that this higher-order phase is an inversion-protected topological crystalline superconductor and study the bulk-boundary correspondence. Finally, we discuss possible experiments for probing the Majorana corner modes. Our findings suggest superconducting monolayer WTe_{2} is a playground for higher-order topological superconductivity and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect.

Strain-Controlled Superconductivity in Few-Layer NbSe2

The controlled tunability of superconductivity in low-dimensional materials may enable new quantum devices. Particularly in triplet or topological superconductors, tunneling devices such as Josephson junctions, etc., can demonstrate exotic functionalities. The tunnel barrier, an insulating or normal material layer separating two superconductors, is a key component for the junctions. Thin layers of NbSe₂ have been shown as a superconductor with strong spin orbit coupling, which can give rise to topological superconductivity if driven by a large magnetic exchange field. Here we demonstrate the superconductor-insulator transitions in epitaxially grown few-layer NbSe₂ with wafer-scale uniformity on insulating substrates. We provide the electrical transport, Raman spectroscopy, cross-sectional transmission electron microscopy, and X-ray diffraction characterizations of the insulating phase. We show that the superconductor-insulator transition is driven by strain, which also causes characteristic energy shifts of the Raman modes. Our observation paves the way for high-quality heterojunction tunnel barriers to be seamlessly built into epitaxial NbSe₂ itself, thereby enabling highly scalable tunneling devices for superconductor-based quantum electronics.

Tunable Flux Vortices in Two-Dimensional Dirac Superconductors

The nontrivial geometry encoded in the quantum mechanical wave function has important consequences for both noninteracting and interacting systems. Yet, our understanding of the relationship between geometrical effects in noninteracting systems and their interacting counterparts is far from complete. Here, we demonstrate how the single-particle Berry curvature associated with the normal phase in two dimensions modifies the fluxoid quantization of a Bardeen-Cooper-Schrieffer superconductor. A discussion of the experimental scenarios where this anomalous quantization is expected is provided. Our work demonstrates the importance of variational Ansätze in making a clear connection between the Berry phases of single-particle and many-body wave functions.

Proximity-Induced Superconductivity in Monolayer MoS2

Proximity effects in superconducting normal (SN) material heterostructures with metals and semiconductors have long been observed and theoretically described in terms of Cooper pair wave functions and Andreev reflections. Whereas the semiconducting N-layer materials in the proximity experiments to date have been doped and tens of nanometers thick, we present here a proximity tunneling study involving a pristine single-layer transition-metal dichalcogenide film of MoS₂ placed on top of a Pb thin film. Scanning tunneling microscopy and spectroscopy experiments together with parallel theoretical analysis based on electronic structure calculations and Green's function modeling allow us to unveil a two-step process in which MoS₂ first becomes metallic and then is induced into becoming a conventional s-wave Bardeen-Cooper-Schrieffer-type superconductor. The lattice mismatch between the MoS₂ overlayer and the Pb substrate is found to give rise to a topographic moiré pattern. Even though the induced gap appears uniform in location, the coherence peak height of the tunneling spectra is modulated spatially into a moiré pattern that is similar to but shifted with respect to the moiré pattern observed in topography. The aforementioned modulation is shown to originate from the atomic-scale structure of the SN interface and the nature of local atomic orbitals that are involved in generating the local pairing potential. Our study indicates that the local modulation of induced superconductivity in MoS₂ could be controlled via geometrical tuning, and it thus shows promise toward the integration of monolayer superconductors into next-generation functional electronic devices by exploiting proximity-effect control of quantum phases.

Recent progress of TMD nanomaterials: phase transitions and applications

Transition metal dichalcogenides (TMDs) show wide ranges of electronic properties ranging from semiconducting, semi-metallic to metallic due to their remarkable structural differences. To obtain 2D TMDs with specific properties, it is extremely important to develop particular strategies to obtain specific phase structures. Phase engineering is a traditional method to achieve transformation from one phase to another controllably. Control of such transformations enables the control of properties and access to a range of properties, otherwise inaccessible. Then extraordinary structural, electronic and optical properties lead to a broad range of potential applications. In this review, we introduce the various electronic properties of 2D TMDs and their polymorphs, and strategies and mechanisms for phase transitions, and phase transition kinetics. Moreover, the potential applications of 2D TMDs in energy storage and conversion, including electro/photocatalysts, batteries/supercapacitors and electronic devices, are also discussed. Finally, opportunities and challenges are highlighted. This review may further promote the development of TMD phase engineering and shed light on other two-dimensional materials of fundamental interest and with potential ranges of applications.

High throughput study on magnetic ground states with Hubbard U corrections in transition metal dihalide monolayers

We present a high throughput study of the magnetic ground states for 90 transition metal dihalide monolayers TMX₂ using density functional theory based on a collection of Hubbard U values. Stable geometrical phases between 2H and 1T are first determined. Spin-polarized calculations show that 50 out of 55 magnetic TMX₂ monolayers are energetically prone to the 1T phase. Further, the magnetic ground states are determined by considering four local spin models with respect to different U values. Interestingly, 23 out of 55 TMX₂ monolayers exhibit robust magnetic ground orderings which will not be changed by the U values. Among them, NiCl₂ with a magnetic moment of 2 μ _B is a ferromagnetic (FM) insulator, while the VX₂, MnX₂ (X = Cl, Br and I), PtCl₂ and CoI₂ monolayers have noncollinear antiferromagnetic (120°-AFM) ground states with a tiny in-plane magnetic anisotropic energy, indicating flexible magnetic orientation rotation. The exchange parameters for both robust FM and 120°-AFM systems are analyzed in detail with the Heisenberg model. Our high-throughput calculations give a systematic study of the electronic and magnetic properties of TMX₂ monolayers, and these two-dimensional materials with versatile magnetic behavior may have great potential for spintronic applications.

Dielectric Properties of NbxW1-xSe2 Alloys

The growth of transition metal dichalcogenide (TMDC) alloys provides an opportunity to experimentally access information elucidating how optical properties change with gradual substitutions in the lattice compared with their pure compositions. In this work, we performed growths of alloyed crystals with stoichiometric compositions between pure forms of NbSe₂ and WSe₂, followed by an optical analysis of those alloys by utilizing Raman spectroscopy and spectroscopic ellipsometry.

Tip-induced superconductivity coexisting with preserved topological properties in line-nodal semimetal ZrSiS

ZrSiS was recently shown to be a new material with topologically non-trivial band structure that exhibits multiple Dirac nodes and a robust linear band dispersion up to an unusually high energy of 2 eV. Such a robust linear dispersion makes the topological properties of ZrSiS insensitive to perturbations like carrier doping or lattice distortion. Here, we show that a novel superconducting phase with a remarkably high [Formula: see text] of 7.5 K can be induced in single crystals of ZrSiS by a non-superconducting metallic tip of Ag. From first-principles calculations, we show that the observed superconducting phase might originate from a dramatic enhancement of density of states due to the presence of a metallic tip on ZrSiS. Our calculations also show that the emerging tip-induced superconducting phase co-exists with the well preserved topological properties of ZrSiS.

Transport evidence of asymmetric spin-orbit coupling in few-layer superconducting 1Td-MoTe2

Two-dimensional transition metal dichalcogenides MX₂ (M = W, Mo, Nb, and X = Te, Se, S) with strong spin-orbit coupling possess plenty of novel physics including superconductivity. Due to the Ising spin-orbit coupling, monolayer NbSe₂ and gated MoS₂ of 2H structure can realize the Ising superconductivity, which manifests itself with in-plane upper critical field far exceeding Pauli paramagnetic limit. Surprisingly, we find that a few-layer 1T_d structure MoTe₂ also exhibits an in-plane upper critical field which goes beyond the Pauli paramagnetic limit. Importantly, the in-plane upper critical field shows an emergent two-fold symmetry which is different from the isotropic in-plane upper critical field in 2H transition metal dichalcogenides. We show that this is a result of an asymmetric spin-orbit coupling in 1T_d transition metal dichalcogenides. Our work provides transport evidence of a new type of asymmetric spin-orbit coupling in transition metal dichalcogenides which may give rise to novel superconducting and spin transport properties.

Mapping multi-valley Lifshitz transitions induced by field-effect doping in strained MoS2 nanolayers

Gate-induced superconductivity at the surface of nanolayers of semiconducting transition metal dichalcogenides (TMDs) has attracted a lot of attention in recent years, thanks to the sizeable transition temperature, robustness against in-plane magnetic fields beyond the Pauli limit, and hints to a non-conventional nature of the pairing. A key information necessary to unveil its microscopic origin is the geometry of the Fermi surface hosting the Cooper pairs as a function of field-effect doping, which is dictated by the filling of the inequivalent valleys at the K/K[Formula: see text] and Q/Q[Formula: see text] points of the Brillouin zone. Here, we achieve this by combining density functional theory calculations of the bandstructure with transport measurements on ion-gated 2H-MoS₂ nanolayers. We show that, when the number of layers and the amount of strain are set to their experimental values, the Fermi level crosses the bottom of the high-energy valleys at Q/Q[Formula: see text] at doping levels where characteristic kinks in the transconductance are experimentally detected. We also develop a simple 2D model which is able to quantitatively describe the broadening of the kinks observed upon increasing temperature. We demonstrate that this combined approach can be employed to map the dependence of the Fermi surface of TMD nanolayers on field-effect doping, detect Lifshitz transitions, and provide a method to determine the amount of strain and spin-orbit splitting between sub-bands from electric transport measurements in real devices.

Evidence of pair-density wave in spin-valley locked systems

Cooper pairs with a finite center-of-mass momentum form a remarkable state in which the superconducting order parameter is modulated periodically in space. Although intense interest in such a "pair-density wave" (PDW) state has emerged due to recent discoveries in high T c superconductors, there is little theoretical understanding of the mechanism driving this exotic state. The challenge is that many competing states lie close in energy in seemingly simple models, such as the Hubbard model, in the strongly correlated regime. Here, we show that inversion symmetry breaking and the resulting spin-valley locking can promote PDWs over more commonly found spin stripes through frustration against magnetic order. Specifically, we find the first robust evidence for a PDW within density matrix renormalization group simulation of a simple fermionic model. Our results point to a tantalizing possibility in hole-doped group VI transition metal dichalcogenides, with spin-valley locked band structure and moderate correlations.

Defect tolerant and dimension dependent ferromagnetism in MnSe2

By performing density functional theory-based calculations, we investigate the structural, vibrational, electronic and magnetic properties of 2D monolayers, nanoribbons and quantum dots of MnSe₂.

Multi-Valley Superconductivity in Ion-Gated MoS2 Layers

Layers of transition metal dichalcogenides (TMDs) combine the enhanced effects of correlations associated with the two-dimensional limit with electrostatic control over their phase transitions by means of an electric field. Several semiconducting TMDs, such as MoS₂, develop superconductivity (SC) at their surface when doped with an electrostatic field, but the mechanism is still debated. It is often assumed that Cooper pairs reside only in the two electron pockets at the K/K' points of the Brillouin Zone. However, experimental and theoretical results suggest that a multivalley Fermi surface (FS) is associated with the SC state, involving six electron pockets at Q/Q'. Here, we perform low-temperature transport measurements in ion-gated MoS₂ flakes. We show that a fully multivalley FS is associated with the SC onset. The Q/Q' valleys fill for doping ≳ 2 × 10¹³ cm^-2, and the SC transition does not appear until the Fermi level crosses both spin-orbit split sub-bands Q ₁ and Q ₂. The SC state is associated with the FS connectivity and promoted by a Lifshitz transition due to the simultaneous population of multiple electron pockets. This FS topology will serve as a guideline in the quest for new superconductors.

An unusual continuous paramagnetic-limited superconducting phase transition in 2D NbSe 2

Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity ¹ . Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties^1-5. Two-dimensional (2D) NbSe₂ has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC)^6-9. Here we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe₂. Using tunelling spectroscopy under high in-plane magnetic fields, we observe a continuous closing of the superconducting gap at the upper critical field at low temperatures, in stark contrast to the abrupt first-order transition observed in BCS thin-film superconductors^10-12. The paramagnetic-limited continuous transition arises from a large spin susceptibility of the superconducting phase due to the Ising SOC. The result is further supported by self-consistent mean-field calculations based on the ab initio band structure of 2D NbSe₂. Our findings establish 2D NbSe₂ as a promising platform to explore novel spin-dependent superconducting phenomena and device concepts ¹ , such as equal-spin Andreev reflection ¹³ and topological superconductivity^14-16.

Tunnelling spectroscopy of gate-induced superconductivity in MoS2

The ability to gate-induce superconductivity by electrostatic charge accumulation is a recent breakthrough in physics and nanoelectronics. With the exception of LaAlO₃/SrTiO₃ interfaces, experiments on gate-induced superconductors have been largely confined to resistance measurements, which provide very limited information about the superconducting state. Here, we explore gate-induced superconductivity in MoS₂ by performing tunnelling spectroscopy to determine the energy-dependent density of states (DOS) for different levels of electron density n. In the superconducting state, the DOS is strongly suppressed at energy smaller than the gap Δ, which is maximum (Δ ~2 meV) for n of ~1 × 10¹⁴ cm^-2 and decreases monotonously for larger n. A perpendicular magnetic field B generates states at E < Δ that fill the gap, but a 20% DOS suppression of superconducting origin unexpectedly persists much above the transport critical field. Conversely, an in-plane field up to 10 T leaves the DOS entirely unchanged. Our measurements exclude that the superconducting state in MoS₂ is fully gapped and reveal the presence of a DOS that vanishes linearly with energy, the explanation of which requires going beyond a conventional, purely phonon-driven Bardeen-Cooper-Schrieffer mechanism.

Pressure induced superconductivity bordering a charge-density-wave state in NbTe4 with strong spin-orbit coupling

Transition-metal chalcogenides host various phases of matter, such as charge-density wave (CDW), superconductors, and topological insulators or semimetals. Superconductivity and its competition with CDW in low-dimensional compounds have attracted much interest and stimulated considerable research. Here we report pressure induced superconductivity in a strong spin-orbit (SO) coupled quasi-one-dimensional (1D) transition-metal chalcogenide NbTe₄, which is a CDW material under ambient pressure. With increasing pressure, the CDW transition temperature is gradually suppressed, and superconducting transition, which is fingerprinted by a steep resistivity drop, emerges at pressures above 12.4 GPa. Under pressure p = 69 GPa, zero resistance is detected with a transition temperature T_c = 2.2 K and an upper critical field μ₀H_c2 = 2 T. We also find large magnetoresistance (MR) up to 102% at low temperatures, which is a distinct feature differentiating NbTe₄ from other conventional CDW materials.

Phase Transitions of the Polariton Condensate in 2D Dirac Materials

For the quantum well in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon (e-ph) coupling can lead to the hybridizations of the exciton and the cavity photon known as polaritons, which can form the Bose-Einstein condensate above a threshold density. Additional physics due to the nontrivial Berry phase comes into play when the quantum well consists of the gapped two-dimensional Dirac material such as the transition metal dichalcogenide MoS_{2} or WSe_{2}. Specifically, in forming the polariton, the e-ph coupling from the optical selection rule due to the Berry phase can compete against the Coulomb electron-electron (e-e) interaction. We find that this competition gives rise to a rich phase diagram for the polariton condensate involving both topological and symmetry breaking phase transitions, with the former giving rise to the quantum anomalous Hall and the quantum spin Hall phases.

Tuning Ising superconductivity with layer and spin-orbit coupling in two-dimensional transition-metal dichalcogenides

Systems simultaneously exhibiting superconductivity and spin–orbit coupling are predicted to provide a route toward topological superconductivity and unconventional electron pairing, driving significant contemporary interest in these materials. Monolayer transition-metal dichalcogenide (TMD) superconductors in particular lack inversion symmetry, yielding an antisymmetric form of spin–orbit coupling that admits both spin-singlet and spin-triplet components of the superconducting wavefunction. Here, we present an experimental and theoretical study of two intrinsic TMD superconductors with large spin–orbit coupling in the atomic layer limit, metallic 2H-TaS₂ and 2H-NbSe₂. We investigate the superconducting properties as the material is reduced to monolayer thickness and show that high-field measurements point to the largest upper critical field thus reported for an intrinsic TMD superconductor. In few-layer samples, we find the enhancement of the upper critical field is sustained by the dominance of spin–orbit coupling over weak interlayer coupling, providing additional candidate systems for supporting unconventional superconducting states in two dimensions.

Monolayer transition-metal dichalcogenide (TMD) is promising to host features of topological superconductivity. Here, de la Barrera et al. study layered compounds, 2H-TaS₂ and 2H-NbSe₂, in their atomic layer limit and find a largest upper critical field for an intrinsic TMD superconductor.

Full superconducting dome of strong Ising protection in gated monolayer WS2

Many recent studies show that superconductivity not only exists in atomically thin monolayers but can exhibit enhanced properties such as a higher transition temperature and a stronger critical field. Nevertheless, besides being unstable in air, the weak tunability in these intrinsically metallic monolayers has limited the exploration of monolayer superconductivity, hindering their potential in electronic applications (e.g., superconductor-semiconductor hybrid devices). Here we show that using field effect gating, we can induce superconductivity in monolayer WS₂ grown by chemical vapor deposition, a typical ambient-stable semiconducting transition metal dichalcogenide (TMD), and we are able to access a complete set of competing electronic phases over an unprecedented doping range from band insulator, superconductor, to a reentrant insulator at high doping. Throughout the superconducting dome, the Cooper pair spin is pinned by a strong internal spin-orbit interaction, making this material arguably the most resilient superconductor in the external magnetic field. The reentrant insulating state at positive high gating voltages is attributed to localization induced by the characteristically weak screening of the monolayer, providing insight into many dome-like superconducting phases observed in field-induced quasi-2D superconductors.

Interaction between H2O, N2, CO, NO, NO2 and N2O molecules and a defective WSe2 monolayer

In this study, the interaction between gas molecules, including H₂O, N₂, CO, NO, NO₂ and N₂O, and a WSe₂ monolayer containing an Se vacancy (denoted as V_Se) has been theoretically studied. Theoretical results show that H₂O and N₂ molecules are highly prone to be physisorbed on the V_Se surface. The presence of the Se vacancy can significantly enhance the sensing ability of the WSe₂ monolayer toward H₂O and N₂ molecules. In contrast, CO and NO molecules highly prefer to be molecularly chemisorbed on the V_Se surface with the non-oxygen atom occupying the Se vacancy site. Furthermore, the exposed O atoms of the molecularly chemisorbed CO or NO can react with additional CO or NO molecules, to produce C-doped or N-doped WSe₂ monolayers. The calculated energies suggest that the filling of the CO or NO molecule and the removal of the exposed O atom are both energetically and dynamically favorable. Electronic structure calculations show that the WSe₂ monolayers are p-doped by the CO and NO molecules, as well as the C and N atoms. However, only the NO molecule and N atom doped WSe₂ monolayers exhibit significantly improved electronic structures compared with V_Se. The NO₂ and N₂O molecules will dissociate directly to form an O-doped WSe₂ monolayer, for which the defect levels due to the Se vacancy can be completely removed. The calculated energies suggest that although the dissociation processes for NO₂ and N₂O molecules are highly exothermic, the N₂O dissociation may need to operate at an elevated temperature compared with room temperature, due to its large energy barrier of ∼1 eV.

Hidden spin polarization in the 1T-phase layered transition-metal dichalcogenides MX2 (M = Zr, Hf; X = S, Se, Te)

The recent discovery of hidden spin polarization emerging in layered materials of specific nonmagnetic crystal is a fascinating phenomenon, though hardly explored yet. Here, we have studied hidden spin textures in layered nonmagnetic 1T-phase transition-metal dichalcogenides MX₂ (M = Zr, Hf; X = S, Se, Te) by using first-principles calculations. Spin-layer locking effect, namely, energy-degenerate opposite spins spatially separated in the top and bottom layer respectively, has been identified. In particular, the hidden spin polarization of β-band can be easily probed, which is strongly affected by the strength of spin-orbit coupling. The hidden spin polarization of ξ-band locating at high symmetry M point (conduction band minimum) has a strong anisotropy. In the bilayer, the hidden spin polarization is preserved at the upmost Se layer, while being suppressed if the ZrSe₂ layer is taken as the symmetry partner. Our results on hidden spin polarization in 1T-phase dichalcogenides, verifiable by spin-resolved and angle-resolved photoemission spectroscopy (ARPES), enrich our understanding of spin physics and provide important clues to search for specific spin polarization in two dimensional materials for spintronic and quantum information applications.

Comprehensive optical characterization of atomically thin NbSe2

Transition-metal dichalcogenides (TMDCs) have offered experimental access to quantum confinement in one dimension. In recent years, metallic TMDCs like NbSe₂ have taken center stage with many of them exhibiting interesting temperature-dependent properties such as charge density waves and superconductivity. In this paper, we perform a comprehensive optical analysis of NbSe₂ by utilizing Raman spectroscopy, differential reflectance contrast, and spectroscopic ellipsometry. These analyses, when coupled with Kramers-Kronig analysis, allow us to extract the dielectric functions of bulk and atomically thin NbSe₂ and relate them to the resonant behavior of the Raman spectra.

Reduction in Step Height Variation and Correcting Contrast Inversion in Dynamic AFM of WS2 Monolayers

A model has been developed to account for and prevent the anomalies encountered in topographic images of transition metal dichalcogenide monolayers using dynamic atomic force microscopy (dAFM). The height of WS2 monolayers measured using dAFM appeared to be increased or decreased, resulting from the interactions between the tip and the surface. The hydrophilic SiO2 substrate appeared higher than the weakly hydrophilic WS2 when the tip amplitude was low or at a high set point (high force). Large amplitudes and low set points corrected the step height inversion, but did not recover the true step height. Removing water from the sample resulted in an order of magnitude reduced variation in step height, but the WS2 appeared inverted except at low amplitudes and high set points. Our model explains the varying step heights in dAFM of TMDs as a result of varying tip-sample interactions between the sample and substrate, in the presence or absence of capillaries. To eliminate contrast inversion, high amplitudes can be used to reduce the effect of capillary forces. However, when capillaries are not present, low amplitudes and high set points produce images with proper contrast due to tool operation in the repulsive regime on both materials.

Ising Superconductivity and Quantum Phase Transition in Macro-Size Monolayer NbSe2

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have a range of unique physics properties and could be used in the development of electronics, photonics, spintronics, and quantum computing devices. The mechanical exfoliation technique of microsize TMD flakes has attracted particular interest due to its simplicity and cost effectiveness. However, for most applications, large-area and high-quality films are preferred. Furthermore, when the thickness of crystalline films is down to the 2D limit (monolayer), exotic properties can be expected due to the quantum confinement and symmetry breaking. In this paper, we have successfully prepared macro-size atomically flat monolayer NbSe₂ films on bilayer graphene terminated surface of 6H-SiC(0001) substrates by a molecular beam epitaxy (MBE) method. The films exhibit an onset superconducting critical transition temperature (T_c^onset) above 6 K and the zero resistance superconducting critical transition temperature (T_c^zero) up to 2.40 K. Simultaneously, the transport measurements at high magnetic fields and low temperatures reveal that the parallel characteristic field B_c//(T = 0) is above 5 times of the paramagnetic limiting field, consistent with Zeeman-protected Ising superconductivity mechanism. Besides, by ultralow temperature electrical transport measurements, the monolayer NbSe₂ film shows the signature of quantum Griffiths singularity (QGS) when approaching the zero-temperature quantum critical point.